G-Draw+&+identify+lines+&+angles,+&+classify+shapes+by+properties+of+their+lines+&+angles

4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 4.G.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. || ===‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7.Look for and make use of structure. || Use technology tools and skills to reinforce classrom concepts and activities. || ===‍‍‍‍‍‍Revised Bloom's Level of thinking === Remembering Understanding Applying || ===‍‍‍‍‍‍Learning Target/Task Analysis === 4.G.1 This standard asks students to draw two-dimensional geometric objects and to also identify them in twodimensional <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">figures. This is the first time that students are exposed to rays, angles, and perpendicular and parallel <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">lines. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen daily. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students do not easily identify lines and rays because they are more abstract.
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Core Standards ===
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Information Technology Standard ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">right angle acute angle  obtuse angle <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">straight angle segment line <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">ray perpendicular lines  parallel lines

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Draw two different types of quadrilaterals that have two pairs of parallel sides? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Is it possible to have an acute right triangle? Justify your reasoning using pictures and words. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">How many acute, obtuse and right angles are in this shape?

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Draw and list the properties of a parallelogram. Draw and list the properties of a rectangle. How are your <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">drawings and lists alike? How are they different? Be ready to share your thinking with the class.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.G.2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Two-dimensional figures may be classified using different characteristics such as, parallel or perpendicular lines <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">or by angle measurement. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Parallel or Perpendicular Lines: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students should become familiar with the concept of parallel and perpendicular lines. Two lines are parallel if <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">they never intersect and are always equidistant. Two lines are perpendicular if they intersect in right angles (90º). <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students may use transparencies with lines to arrange two lines in different ways to determine that the 2 lines <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">might intersect in one point or may never intersect. Further investigations may be initiated using geometry <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">software. These types of explorations may lead to a discussion on angles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Parallel and perpendicular lines are shown below:

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard calls for students to sort objects based on parallelism, perpendicularity and angle types. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Do you agree with the label on each of the circles in the Venn diagram above? Describe why some shapes fall in <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the overlapping sections of the circles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Draw and name a figure that has two parallel sides and exactly 2 right angles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">For each of the following, sketch an example if it is possible. If it is impossible, say so, and explain why or show <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">a counter example. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• A parallelogram with exactly one right angle. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• An isosceles right triangle. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• A rectangle that is not a parallelogram. (impossible) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• Every square is a quadrilateral. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• Every trapezoid is a parallelogram.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Identify which of these shapes have perpendicular or parallel sides and justify your selection. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">A possible justification that students might give is: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">The square has perpendicular lines because the sides meet at a corner, forming right angles.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Angle Measurement: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This expectation is closely connected to 4.MD.5, 4.MD.6, and 4.G.1. Students’ experiences with drawing and <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">identifying right, acute, and obtuse angles support them in classifying two-dimensional figures based on specified <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">angle measurements. They use the benchmark angles of 90°, 180°, and 360° to approximate the measurement of <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">angles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Right triangles can be a category for classification. A right triangle has one right angle. There are different types <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">of right triangles. An isosceles right triangle has two or more congruent sides and a scalene right triangle has no <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">congruent sides. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.G.3 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">lines of symmetry. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard only includes line symmetry not rotational symmetry. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">you think there would be for regular polygons with 9 and 11 sides. Sketch each figure and check your <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">predictions. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Polygons with an odd number of sides have lines of symmetry that go from a midpoint of a side through a vertex.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍I can...
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can identify points, lines, line segments, rays, and angles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can identify parallel and perpendicular lines and distinguish between the two. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can identify points, lines, line segments, rays, and angles in a 2 dimensional shape. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can identify parallel and perpendicular lines in a 2 dimensional shape. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can sort two dimensional shapes based on specific criteria. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can recognize that triangles can be classified based on the lenghts of their sides. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can identify a triangle based on the size of its angles. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can recognize lines of symmetry in 2 dimensional figures.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Essential Vocabulary
===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">acute angle, right angle, obtuse angle, points, lines, line segments, rays, perpendicular, parallel, right triangles, line of symmetry, line symmetrical figures ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Sample Assessments
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students locate examples of each geometric term in the classroom, take pictures of the examples outside, or cut out pictures of examples from a magazine. Create a geometric collage using what students found.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students use the angle finder created in class. Teacher calls out angles formed by parts of the circle—½, ¼, <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">3/4—and students create the angles with their finders. Teacher could extend the activity by showing other angles and asking students to form a similar degree angle with the finders. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Problem Task: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students will use their angle finder to locate and identify angles in real-life settings (i.e., classroom, playground, home). Students will trace the measurement of the angle finder to represent the measurement of the angle. Students will label the representation with rays, vertex, and interior arc. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Working with partners, students draw several angles and have partners measure them, and vice versa. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Measure the angles of a regular polygon—students understand that angles are equal. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students will locate angles in the classroom or outside. After writing down the angle measurement and item, the students will draw each of the angles found using a protractor. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Ruby is standing on first base. Jasmine is standing on second base. What is the angle of measure from home plate between the two girls? What is the angle between third base and second base? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Answer: 45° <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Bella and Edward’s teacher told them that the two outside rays in this drawing are perpendicular. She asked them to find the missing measure. What is it? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Answer: 45° (again!)

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Give students several pictures of various two-dimensional figures. Practice finding figures by giving students criteria for classifications (i.e., parallel lines, perpendicular lines, acute angles, obtuse angles, and right angles). Finally, have the students identify the right triangles and classify these into a separate group. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Create an art project using all of the new geometric classification terms. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Give students different two-dimensional figures and have them classify them and justify their classification.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Intervention:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://daretodifferentiate.wikispaces.com/Choice+Boards <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.ixl.com/math/grade-4/parallel-perpendicular-intersecting

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Read Straight Lines, Parallel Lines, Perpendicular Lines

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Read The Dot and the Lineby Juster.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">media type="custom" key="19632468"

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Enrichment:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.teachertube.com/viewVideo.php?title=angles_in_a_circle&video_id=231281

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Math quiz using angles and degrees: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.ixl.com/math/grade/4

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Finding degrees of angles: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.mathisfun.com/angles.html

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students use grid to draw parallel, perpendicular, & intersecting lines and plot coordinates for each. They can also find the coordinates for the missing sides of various polygons. They could also draw lines parallel or perpendicular <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">to a line you assign them to plot.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Instructional Resources
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.uen.org/Lessonplan/preview.cgi?LPid=11235 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://illuminations.nctm.org/LessonDetail.aspx?ID=L270

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Using previous knowledge of angle measure, students will be able to view the diagrams at the right, and determine the missing angles.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Using protractors, students will draw angles with missing measure and trade drawings with a partner. The partner will then solve for the missing angle.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.mathsisfun.com/geometry/complementary-angles.html

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.mathsisfun.com/geometry/supplementary-angles.html

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://www.khanacademy.org/video/complementary-and-supplementary-angles?playlist=Geometry

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Book:

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Sir Cumference and the Great Knight of Angleland, by Cindy Neuschwander

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">[[file:Geometric Lines.pptx]]
===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Notes and Additional Information ===